Abstract
A fraction-dense (semi-prime) commutative ring A with 1 is one for which the classical quotient ring is rigid in its maximal quotient ring. The fraction-dense f-rings are characterized as those for which the space of minimal prime ideals is compact and extremally disconnected. For Archimedean lattice-ordered groups with this property it is shown that the Dedekind and order completion coincide. Fraction-dense spaces are defined as those for which C (X) is fraction-dense. If X is compact, then this notion is equivalent to the coincidence of the absolute of X and its quasi-F cover.
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Hager, A.W., Martinez, J. Fraction-dense algebras and spaces. Acta Appl Math 27, 55–65 (1992). https://doi.org/10.1007/BF00046636
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DOI: https://doi.org/10.1007/BF00046636